Q: Why is $-2-3(-1)^{2/3} = -5$? Have I gone mad? Consider this:
$$f(x) = -2-3x^{\frac {2}{3}}$$
Why would $f(-1) = -5$?
Doesn't make sense to me. $f(-1)$ equals $1$ when plugging it in on my calculator. But in my book and when plotting this using google's plot feature (just google this: "-2-3(x^(2/3))" and hover over $-1$), I get $f(-1) = -5$?

A: How do you define $(-1)^{2/3}$? That is the crux.

A: Likely, you will want to consider:
$(-1)^{2/3}=\sqrt[3]{-1^2}=\sqrt[3]{1}=1$ or 
$(-1)^{2/3}=(\sqrt[3]{-1})^2=(-1)^2=1$.
In either case, from here $f(-1)=-2-3(1)=-5$.

A: We can write  $-1^\frac23$ as $(-1^2)^\frac13$  which is equal to $\sqrt[3]1$ which is 1. So $-2 - 3(1) = -5$.
Note that it doesn't matter what you do first whether the cube root or the square. $\sqrt[3]{-1} = -1$ and ${(-1)}^2 = 1$. So you still get the same answer $-5$
